The tech giant's request to add patent infringements to the existing case may be in response to a motion Samsung filed Oct. 1,which added Apple's iPhone 5 to a list of grievances in the same case.

The South Korean technology alleged in its motion that the new iPhone infringed on eight of its patents.

The constant flurry of complaints between the two companies underscores how their patent battles aren't coming to an end anytime soon — even though both companies have suffered legal losses in previous face-offs against one another.

In August, Samsung was ordered to pay Apple $1.05 billion in a California court when it lost a separate lawsuit that dealt primarily with design patents.

Apple, however, has also lost against Samsung. In October, the iPad maker lost an appeal against Samsung in a U.K. case over design patents. Apple was ordered to issue a formal apology statement about how Samsung did not actually copy its iPad designs.

Costly and embarrassing legal decisions haven't deterred either company from their battle to beat the other, and become the dominant player in the billion-dollar smartphone market. Still, Apple's latest move to try and drag Google's Android OS in its battle with Samsung may signal the Cupertino-based company is also ready to take on the search giant.

As the New York Times reported in late August, it may be easier for Apple to go after phone makers in lawsuits, because damages can be determined by the number of phones a company sold that were made using infringed patents.

If Apple wants to go after Google's software, however, a lawsuit is more difficult.

Google doesn't profit from selling its Android software to phone manufacturers. Instead, the company gives its operating software to phone makers like Samsung for free, then makes money by selling ads, apps and other media on its platform.

Yet because of how Google makes money on its Android software, Apple could struggle in a lawsuit to prove that Google financially benefits from patent infringement.

Still, it's too soon to tell just how hard Apple plans to go after Google in its current case against Samsung, and it won't be clear for while. The case isn't expected to go to trial until 2014.